It may be useful to recall the Ehresmann method of setting up the exponential law for categories using the double categoy of commuting squares in a category. This is also written up in (R.Brown, P. NICKOLAS), ``Exponential laws for topological categories, groupoids and groups and mapping spaces of colimits'', {\em Cah. Top. G\'eom. Diff.} 20 (1979) 179-198. The nice point is that the category structure is induced by a double category composition, and so if you have extra structure, such as a topology, that carries over. Ronnie Brown On Tue, 3 Jun 2003, Toby Bartels wrote:
Steve Vickers wrote:
It is also possible to use a 2-dimensional syntax, in which horizontal composition is composed horizontally and vertical composition is composed vertically. Then algebraic manipulations are a bit like sliding tiles around in a tray.
Of course this can be done using big diagrams. But is there a tight syntax for this just using text? Can you point to an example? (preferably a TeX source online, but a printed page in a regular journal would also work).
-- Toby
Prof R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Centre for the Popularisation of Mathematics Raising Public Awareness of Mathematics CDRom Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/centre/index.html